The earliest evolutionary stages of the universe and space-time torsion

A model of the early universe is proposed on the basis of Einstein-Cartan theory. The evolution of the universe begins from the primary static stage. The problems of gravitational stability are investigated.     

Planck's constant,torsion, and space-time defects

A possible way of building Planck's constant into the structure of space-time is considered. This is done by assuming that the torsional defect that intrinsic spin produces in the geometry is a multiple of the Planck length.     

Quantized space-time,torsion, and magnetic monopoles

Within the tetrad formalism we introduce quantized space-time in the curvilinear case by using general coordinate transformations with noncommuting terms. Fermion and boson fields are studied and the affine connection is also defined in this space. It is shown that space-time torsion and magnetic monopoles appear as consequences of the theory with quantized space-time at small distances. This method may open a new way of understanding topological structure of space-time.     

史瓦西时空中自由粒子的运动方程

直接求解史瓦西时空中自由粒子的测地线方程,得出粒子运动方程的一般常见形式.此方法与一般教材中根据史瓦西度规的静态球对称性以及四速归一条件得出的运动方程完全相同.此方法物理意义更清晰、明确,同时对理解弯曲时空中的测地线方程具有重要意义.     

General equations of motion for test particles in space-time with torsion

The momentum and spin equations of motion for test particles possessing different spins in space-time with torsion are derived from the most general functional form of _M . The same kinds of equations in general relativity and in Kibble's gauge theory of gravitation are special cases of our equations.     

On the structure of space-time caustics

Caustics formed by timelike and null geodesics in a space-timeM are investigated. Care is taken to distinguish the conjugate points in the tangent space (T-conjugate points) from conjugate points in the manifold (M-conjugate points). It is shown that most nonspacelike conjugate points are regular, i.e. with all neighbouring conjugate points having the same degree of degeneracy. The regular timelikeT-conjugate locus is shown to be a smooth 3-dimensional submanifold of the tangent space. Analogously, the regular nullT-conjugate locus is shown to be a smooth 2-dimensional submanifold of the light cone in the tangent space. The smoothness properties of the null caustic are used to show that if an observer sees focusing in all directions, then there will necessarily be a cusp in the caustic. If, in addition, all the null conjugate points have maximal degree of degeneracy (as in the closed Friedmann-Robertson-Walker universes), then the space-time is closed.     

Homogeneous isotropic cosmological model of space-time with torsion in the Einstein-Cartan theory of gravitation

A systematic treatment is applied to the cosmological problem in the Einstein-Cartan theory of gravitation on the basis of the variational principle formulated previously for an ideal fluid in space with torsion. Exact solutions are obtained for homogeneous isotropic cosmological models with flat three-dimensional space filled with powdery matter and a fluid with an equation of state p=/3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 24–28, March, 1977.The author thanks Professor D. D. Ivanenko and members of the seminar conducted by him for useful discussions.     

Localization of the Einstein group and a nonsingular cosmological model of space-time with torsion

We consider an Einstein-invariant gauge theory of gravitation (EGT), obtained by localizing the group of motions of a homogeneous static Einstein Universe. Taking into account the cosmological term, we find exact solutions of EGT are as nonsingular homogeneous Isotropic cosmological models with both the metric and the torsion regular. It is shown that EGT satisfies the principle of correspondence with Newton's theory of gravity and with the tetrad theory of gravity in the space of absolute parallelism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fisika, No. 10, pp. 13–17, October, 1986.     

Rotation and acceleration as parallel transport in a space-time with torsion

We demonstrate that two simple noninertial motions, namely, uniformly rotating and uniformly accelerated motions, can be described as parallel transports, in a space-time manifold with torsion, of the moving object's reference frame along its world line. On the basis of that, it is conjectured that the electromagnetic field tensor is really only the temporal part of the contortion tensor. The only disturbing feature is that the decrease of the electromagnetic/gravitational coupling ratio with velocity (by the factor ) does not appear in this approach.     

On the theory of space-time polarization holography

Polarization holographic recording and the reconstruction of the field of a nonstationary object wave are considered theoretically. Expressions for the nondiffracted beam, as well as the virtual and real images, formed by a space-time polarization hologram are analyzed. It is shown that, under certain conditions imposed on the isotropic, anisotropic, and gyrotropic responses of a polarization-sensitive medium, one can adequately reconstruct the space structure, time waveform, and polarization characteristics of the field of a nonstationary object in the virtual image.     

On the space-time content of Liouville-type theories

An analysis of the space-time content of the Liouville-type field theories (LFT) is presented. The origin and significance of D=2, D=26 and, respectively, D=10 are rigorously explained and connections between LFT, octonionic algebra and N=8 D=4 supergravity are derived. As byproducts, new approaches to (justification of) internal symmetries and, respectively, implementation of the Kaluza-Klein idea (i.e., ‘physics from higher dimensions’) are suggested.     

Renormalization of a quantum field theory model in a curved space-time with torsion

A quantum field theory model that contains interacting non-Abelian gauge fields, scalar fields, and spinor fields is considered in a curved space-time with torsion. The cone-loop counterterms are found. It is shown that the multiplicative renormalization condition requires a nonminimal coupling of the matter with the gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 94–100, August, 1985.     

On space-time permeated by the perfect magnetofluid

A space-time permeated by the self-gravitating perfect fluid with infinite electrical conductivity and constant magnetic permeability (perfect magnetofluid) is investigated. For aC space defined as the space in which the divergence of conformal curvature vanishes, it is proved that the rotation explicitly depends on the magnetic field. In aJ space characterized by the vanishing of the divergence of Petrov space-matter tensor, the invariance of the energy density, the isotropic pressure, and the magnitude of the magnetic field along the divergence-free magnetic lines is established. It is found that if the stress-energy tensor of the perfect magnetofluid is a Killing tensor, the energy density, the isotropic pressure, and the magnitude of the magnetic field are constant. Moreover it is shown that the stream lines are expansion-free and the magnetic lines are divergence-free. It is proved that the complexion of the field of the perfect magnetofluid remains invariant along the magnetic lines if and only if these lines are normal to the lines of vorticity.     

On the continuity of causal automorphisms of space-time

We prove that any causal automorphism of the (curved or not) space-time in any dimension is continuous.     

Two-component neutrino field and spherical symmetry in a space-time with curvature and torsion

The incompatibility of the spherical symmetry of a space-time with the presence of a “classical” i.e. not-quantized, 2-component neutrino field is extended from the purely Riemannian to the Riemann-Cartan geometry, corresponding to a space-time with curvature and torsion.     

On non-static axially symmetric space-time

In this paper the general non-static axially symmetric line element has been considered in the context of Petrov Classification. The space-time is found to be of various Petrov Types under different circumstances. The necessary algebraic conditions for such a space-time to be of class one have also been derived. It is found that there exists only one solution representing a plane symmetric class-one null-electromagnetic field.     

On a microscopic representation of space-time

We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low-energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of the operator actions. Then we discuss the geometrical origin of this noncompact Lie algebra and ??reduce?? the geometry in order to introduce in each of these steps coordinate definitions which can be related to an algebraic representation in terms of the spontaneous symmetry breakdown along the Lie algebra chain su*(4) ?? usp(4) ?? su(2) × u(1). Standard techniques of Lie algebra decomposition(s) as well as the (physical) operator identification give rise to interesting physical aspects and lead to a rank-1 Riemannian space which provides an analytic representation and leads to a 5-dimensional hyperbolic space H ₅ with SO(5, 1) isometries. The action of the (compact) symplectic group decomposes this (globally) hyperbolic space into H ₂ ?? H ₃ with SO(2, 1) and SO(3, 1) isometries, respectively, which we relate to electromagnetic (dynamically broken SU(2) isospin) and Lorentz transformations. Last not least, we attribute this symmetry pattern to the algebraic representation of a projective geometry over the division algebra H and subsequent coordinate restrictions.     

On the reality of space-time geometry and the wavefunction

The action-reaction principle (AR) is examined in three contexts: (1) the inertial-gravitational interaction between a particle and space-time geometry, (2) protective observation of an extended wave function of a single particle, and (3) the causal-stochastic or Bohm interpretation of quantum mechanics. A new criterion of reality is formulated using the AR principle. This criterion implies that the wave function of a single particle is real and justifies in the Bohm interpretation the dual ontology of the particle and its associated wave function. But it is concluded that the Bohm theory is not dynamically complete because the particle and its associated wave function do not satisfy the AR principle.     

Berry phase for spin-1/2 particles moving in a space-time with torsion

Berry phase for a spin-1/2 particle moving in a flat space-time with torsion is investigated in the context of the Einstein–Cartan–Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks. Received: 12 February 2001 / Revised version: 2 May 2001 / Published online: 29 June 2001